2002/12/31 by Jürg Fröhlich, Juerg Froehlich, Marco Merkli +1 · 3 citations
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Quantum and electron transport phenomena #Quantum many-body systems #math-ph #math.MP #msc:82C10 #msc:82C21 #msc:82C35 #msc:82C70
paper · pdf · doi:10.1007/s00023-003-0150-8
published as Ann. Henri Poincaré 4, 897-945 (2003) · 55 pages; 2 figures
arxiv created 2003/04/15 · openalex publication_date 2003/10/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
The general theory of simple transport processes between quantum mechanical reservoirs is reviewed and extended. We focus on thermoelectric phenomena, involving exchange of energy and particles. Entropy production and Onsager relations are relevant thermodynamic notions which are shown to emerge from the microscopic description. The theory is illustrated on the example of two reservoirs of free fermions coupled through a local interaction. We construct a stationary state and determine energy- and particle currents with the help of a convergent perturbation series. We explicitly calculate several interesting quantities to lowest order, such as the entropy production, the resistance, and the heat conductivity. Convergence of the perturbation series allows us to prove that they are strictly positive under suitable assumptions on the interaction between the reservoirs.